.5x^2-1.25x-1.75=0

Solution for .5x^2-1.25x-1.75=0 equation:

Simplifying
0.5x2 + -1.25x + -1.75 = 0

Reorder the terms:
-1.75 + -1.25x + 0.5x2 = 0

Solving
-1.75 + -1.25x + 0.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.5 the coefficient of the squared term: 

Divide each side by '0.5'.
-3.5 + -2.5x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -2.5x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -2.5x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -2.5x + x2 = 0 + 3.5
-2.5x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-2.5x + x2 = 3.5

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 3.5 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 3.5 + 1.5625

Combine like terms: 3.5 + 1.5625 = 5.0625
1.5625 + -2.5x + x2 = 5.0625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 5.0625

Calculate the square root of the right side: 2.25

Break this problem into two subproblems by setting 
(x + -1.25) equal to 2.25 and -2.25.

Subproblem 1
x + -1.25 = 2.25

Simplifying
x + -1.25 = 2.25

Reorder the terms:
-1.25 + x = 2.25

Solving
-1.25 + x = 2.25

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 2.25 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 2.25 + 1.25
x = 2.25 + 1.25

Combine like terms: 2.25 + 1.25 = 3.5
x = 3.5

Simplifying
x = 3.5

Subproblem 2
x + -1.25 = -2.25

Simplifying
x + -1.25 = -2.25

Reorder the terms:
-1.25 + x = -2.25

Solving
-1.25 + x = -2.25

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -2.25 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -2.25 + 1.25
x = -2.25 + 1.25

Combine like terms: -2.25 + 1.25 = -1
x = -1

Simplifying
x = -1

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.5, -1}